Load assigning apparatus for electric power systems



Nov. 18, 1958 w. R. BROWNLEE LOAD ASSIGNING APPARATUS FOR ELECTRIC POWERSYSTEMS 5 Sheets-Sheet 1 Filed Jan. 7, 1957 .QE .w23 ENSS 29.59255 $232069225: 8252.6; .259m ..5 552252 INVENTOR. WILLIAM R. BROWN LEE ATTORNEY.

Nov. 18, 1958 w. R. BROWNLEE LOAD ASSIGNING APPARATUS FOR ELECTRIC POWERSYSTEMS 5 Sheets-Sheet 2 Filed Jan. '7, 1957 W. R. BROWNLEE Nov. 18,1958 LOAD ASSIGNING APPARATUS FOR ELECTRIC POWER SYSTEMS Filed Jan. '7,1957 5 Sheets-Sheet 3 Nov. 18, 1958 W. R. BROWNLEE LOAD ASSIGNINGAPPARATUS FOR ELECTRIC POWER SYSTEMS Filed Jan. 7, 1957 5 Sheets-Sheet 4rn T l LOAD ASSIGNING APPARATUS FOR ELECTRIC POWER SYSTEMS 5Sheets-Sheet 5 Filed Jan. 7, 1957 Y INVENTOR.

WILLIAM R. BROWNLEE ATTORNEY.

United States Iiatent i LOAD ASSIGNING APPARATUS Fon ELECTRIC f POWERSYSTEMS William R. Brownlee, Birmingham, Ala.

Application January 7, 1957, Serial No. 632,807 17 claims. (el. sur-57)The present invention relates generally to the assign mentor the loadsto the interconnected generating plants of an electric power generatingand distributing system in such a manner as to maintain at a minimum thecost of the total delivered energy in the system, and hence to providethe most economical operation of the system. I

Specifically, the invention relates to methods and apparatus forautomatically effecting such assignment of the plantloads in accordancewith the incremental costs or delivered energy for the plants so as tocoordinate the'incremental generating costs and incremental transmissionlosses in the vsystem to the end of securing Vthe most economicalcombination of plant loadings.`

More specifically, the present invention pertains to methods andapparatus of the stated type wherein the loads or outputs of thecontrolled system plants are controlled automatically as necessary toequalize the incremental costs of delivered energy for the plants, andhence to maintain the plants in economic balance, to the end ofachieving an optimum plant loading schedule, and "the most economicalsystem operation.l

A general object of the present invention is to provide animprovedmethod and apparatus for use in assigning the loads to theinterconnected generatingplantsof an electric power generating andydistributing system in accordance with the incremental costs' ofdelivered energy for the plants so as to coordinate the incrementalAtrans'- mission losses and incremental generating costsy in the systemto the end of securing the most economical loading of the system plantsand the most economical operation of the system. r

A specific object of the invention is to provide novel apparatus of theforegoing type which determines at each of selected ones of the systemplants the amount and direction, if any, by which the outputof the plantmust be changed in order to maintain equality between ythe incrementalcosts of delivered energy for the system plants, and hence to maintain`the plants in economic balance, for the existing system conditions.

A more specific object of the invention is to provide novel apparatus ofthe type just described which produces at each selected system plant adeviation ellect representative or any departure from equality betweenthe incremental cost of delivered'energy for the plant and theincremental cost of delivered energy commonto y"the others of the systemplants at that time, and hence representative of'any deviation oftheplant from economic balance 'with respect to the other plants, saiddeviation eiie'ct being a measure of the/amount and direction by whichthe'plant voutput must be changed in order to obtain equality betweenthe incremental costs of delivered energy `for the plants, and economicbalance between the plants, for the existing system 'conditions "A"still" more speclfieobject of the Hinvention is to provide novel'apparatus as just specied which "produces at each selected system plantan effect which is ameasure of the hincremental transmission vloss forthe plant with respect to achose'n common 'reference point in thesystem,

2,861,196 Patented Nov. 1,8, 1958 'ice 2 andwhich effects a comparisonat each of these` plants between said loss effectand an effect producedat the plant which is a measure of the incremental generating costforthe plant with respect to said reference point, said loss and cost,effects being equal when the plant is in economic balance and has lthesame incremental cost of delivered energyas the other system plants.

An even more specific object of the invention is to provide novelapparatusiof'the type just described which detects atieach plant,`bymeans of said comparison, any deviation between the loss and cost eiectsproduced at the plant, and which utilizes this'detected deviation toproduce said deviation effect Lwhich is representative of any deviationor departure of the plant from economic balance. A still more specificobject of the invention is to provide novel apparatus as just'speciiiedwherein each of said incremental transmission loss effects is producedor computed at the corresponding plant in the form of an incrementaltransmission loss ratio for the plant with respect to said commonreference point, wherein each of said ratios is a function of solely (1)the phase angle between the bus voltage of the corresponding plant and acommon reference voltage individual to said reference point, and (2) theconstant ratio of'the reactance to the resistance of the equivalent pathor transfer impedance between` the corresponding plant and saidreference point, and wherein each of said incremental generating vcosteffects is computed at the corresponding plant in the forni of anincremental generating cost ratio for the plant with respect to saidreference point, for comparison atthe plant with Vthe correspondingincremental transmission lossratio. v

lt is also a specific object of the invention to provide novel apparatusand vcircuitry for effecting the foregoing computations, comparisons,detections, and deviation effect production.

YAnother specific object of the invention is to provide novel apparatusof the foregoing type Where in a' single common master reference signalis supplied to all ofthe selected system plants for coordinatingthe`production at the plants of said deviation effects which arerepresenta-` tive of departures of the plants from economic balance Witheach other.

A more specific object of the invention is to provide novel apparatus asjust specified wherein the phase of said master reference signal is thesame at all plants, and wherein said phase angle at each plant,whichdeter-4 mines said incremental transmission loss ratio for theplant, is the phase angle between the bus voltage of the plant and saidreference signal.

An even more specific object of the invention is to provide novelapparatus as just specified whereinithe phase of said reference signalhas la'valu'e whicnis Varied in accordance withdeviation between desiredanderristing operating conditionsy in the system.

Another specific object of the'invention is to provide novel apparatusof the foregoing type which automatically controls the output of each ofthe selected system plants, in accordance with said deviation effectproduced at the plant, as necessary to maintain equal the incrementaltransmission loss and generating cost effects for the plant, and'thus tomaintain the plant in economic balance with respect 'to said'referencepoint and'henee the others of the system plants.

Still another specific object of the invention is to provide a novelmethod and apparatus of the type specified herein for `determiningftheincremental value or cost of energy at Aa locationor point in thesystem, other than a plant, by relating this value of energy at saidpoint to the known energy value at some other system point, such as saidcommon reference point.

Finally, it is a specific object of the invention to provide a noveleconomic load assigning method and apparatus of the foregoing characterwherein a common master reference signal is sent to all of the systemplants to be controlled, wherein this signal is utilized at each plantin the control of the plant output as necessary to coordinate theincremental cost of delivered energyY for the plant with those of theother system plants to the end of equalizing these incremental deliveredenergycosts and hence producing the most economical combination of plantoutputs, and wherein said signal also controls the output of each plantas necessary to correct for deviations between actual and desired systemoperating conditions, whereby the selected system plants are loadedautomatically in the manner necessary to provide at all times thedesired system operating conditions in the most economical manner.

It has been recognized in the past that the maintenance of an optimumgenerating or loading schedule in a power system, for maintainingeconomical system operation and a minimum cost of total delivered energyin the system, requires the continual coordination of the systemgenerating costs and transmission losses. To this end, various methodshave been developed in the past for obtaining system transmission lossconstants, usually referred to as B-type constants, and arrangementshave been described for applying these constants to system loadscheduling or dispatching problems. These applications have usuallyinvolved the comparison of incremental fuel costs and incrementaltransmission losses in arriving at the optimum generating schedules tobe followed, the incremental transmission losses being calculated on thebasis of the previously determined B-type constants mentioned above.

As is well known to those skilled in the art, the foregoing previouslyknown and used methods of calculating and coordinating incremental costsand losses for arriving vat optimum generating schedules are subject tonumerous significant disadvantages. These disadvantages are due,primarily, to the frequently unsatisfactory nature of the B-typeconstants, to the practical diiculties encountered in obtaining suchconstants, and to the complexity of the computations involved inapplying the constants to the problem and in solving the resultingsimultaneous equations.

I have discovered, however, a novel method for determining incrementaltransmission losses which is not subject to the above-noteddisadvantages associated with the B-type loss constants and their use inobtaining optimum generating schedules. Specically, I have discoveredthat a unique relationship exists between the incremental transmissionloss between two points and the phase angle between the voltages atthese points. More specifically, I have discovered that the incrementaltransmission loss (dL dP between two plants can be expressed as afunction of solely the phase angle between the bus voltages of the twoplants and the constant ratio of reactance to resistance (K) of theequivalent path joining the two plants. This unique relationship hasbeen described, developed, and explained in my paper entitledCo-ordination of Incremental Fuel Costs and Incremental TransmissionLosses by Functions of Voltage Phase Angles which appeared at pages 529to 533 of part III-A, Power Apparatus and Systems, of volume 73 of theAIEE Transactions. In that paper, I have shown that the followingincremental transmission loss equation properly defines the incrementaltransmission loss between two plants in terms of solely the factorsnoted and defined above:

Q 2 sin 8 dP-K cos -l-sin 0 I have also shown in the above-mentionedpaper that Ithis unique expression for incremental transmission loss canbe utilized to advantage in a practical comparison method which I havedeveloped for determining, in an accurate but relatively simple manner,when the plants of a system, and hence the entire system, are ineconomic balance, and hence when the system is operating at a minimumcost of total delivered energy. Specifically, I have shown in said paperthat the Plants l and 2 of any given pair of plants of a system willhave the same incremental cost of delivered energy at any given point,and hence will be in economic balance, when the following economicbalance equation, relating the incremental generating costs andincremental transmission losses for the two plants, is satisfied:

dFl/dPl-K cos 6l-sin 0 wherein: dFl/dPl and dF2/dP2 are the incrementalgenerating costs for Plants 1 and 2, respectively, K is the abovereactance-resistance ratio of the transfer impedance or equivalent pathbetween the two plants, and 0 is the phase angle by which the busvoltage at Plant l leads the bus voltage at Plant 2.

As pointed out in said paper, the foregoing balance equation for a pairof plants compares the incremental transmission loss ratio between theplants, as determined by my foregoing incremental transmission lossequation, with the incremental generating cost ratio for the plants.Thus, when this balance equation is satisfied, the corresponding plantsoperate at the same incremental cost of delivered energy at any givenpoint, and are in economic balance. Further, when all pairs of thesystem plants are in such economic balance, the entire system is ineconomic balance.

The foregoing phase angle loss computing and comparison method fordetermining when the pairs of plants of a system are in economicbalance, and when the entire system is in balance, is, and is describedin said paper as being, a method which was developed for use insimplifying the adequate planning of power system expansion. I havediscovered, however, that this method also constitutes a highlyeffective, advantageous, and practical tool of relative simplicity foruse in assigning the loads to the plants of an actual, operating systemso as to provide optimum generating or loading schedules and economicalsystem operation under the actual system loading and operatingconditions, inasmuch as the practice of this method requires a knowledgeof only three readily obtainable factors: namely, plant incrementalgenerating costs, constant reactance to resistance ratios, and plant busvoltage phase angles. Moreover, the use of this method in the abovemanner does not involve the disadvantages encountered with the use ofthe previously known methods employing the B-type loss constants, sincethe present method is not subject to the deficiencies inherent in theprior methods. These factors, together with the basic concepts involvedin my comparison method, make this method a highly desirable andpractical one for use in apparatus invented by me for automaticallydetermining when the plants of an operating system are in economicbalance, for computing what changes, if any, in the plant loadings areneeded to provide the most economical combination of plant loadings, andfor automatically controlling the loading of the plants in accordancewith the computed optimum loading data.

Accordingly, in my copending application Serial No. 632,917, led on evendate herewith, I have disclosed and claimed novel apparatus invented byme which is operative in accordance with the foregoing incrementaltransmission loss and balance equations and comparison method to produceeffects representative of the incremental transmission less ratio for apair of interconnected generating plants, to detect deviation fromeconomic balance between pairs of such plants, and to assign the loadsto such plants in relation to the incremental costs of delivered energyfor the plants.

As explained in the aforementioned application, the

satur @f tbs load assigning netbsd. and slrtlis' die closed thereinmakes it desirable, when sele ng n pa "s of plants between which theincrement sts and ISes are to be compared, t0 choose, for the plants ofeach pair, plants which are adjacent electricallyeso as to minimi'jxethe influence of intervening plants on the compnted incremental losses.I have discovered, however, a unique expression which accurately relatesthe incremental transmission loss between two plants to thephase anglebetween the bus voltages of the plants notwithstanding the presence kofintermediate generation along the path interconnecting the two plants.Y'

Specifically, this' new expression ,for lthe incremental transmissionloss between two plants takes hinto account the effect or influenceexerted on the incremental loss by a typical intermediate generatingplant.` In other words, this expression is based on the assumption thatthere is an intermediate plant on the line connecting the two plantsbetween which it is desired to determine the incremental transmissionloss, and the expression is therefore arranged to provide a measure ofthe true incremental transmission loss between said two plants, takinginto 'ac-r count the influence of an intermediate plant.

This novel two-step or two-section expression or equation for theincremental transmission loss between two plants is derived anddeveloped from my foregoing simple or singleastep loss equation byapplying the latter in two successive steps in the manner shown inAppendix I of my aforementioned paper, wherein the derivation of thistwo-step equation is set forth. As shown in said paper, this equationis: I

is the incremental transmission loss between the two plants in questionwhich is to be determined by means of the equation, and wherein 0 and Kare the respective phase angle between the plant bus voltages and thecon stant ratio of reactance to resistance or equivalent path betweenthe plants, all as for the single-step loss equation as set forthhereinbefore. It is apparent that this twostep loss equation, like its`single-step forerunner, provides a measure of the incrementaltransmission loss in terms of or as a function of solely the phase angle0 and the constant K.

I have found that the procedure on which this two-step equation isbased, of treating each pair of plants as if there were one intermediateplant on a direct linebetween them, renders the equation adequatelyaccurate for use in calculating the incremental transmision loss betweenpractically any two plants ofthe system, since it provides accurateresults for both closely and Widely spaced plants, either with o-rwithout intermediate or intervening generation on the line between them.In the case of plants which are near to each other, the phase anglesare'relatively small, so that there is practically no difference in theloss values obtained by the single-step and two-step equations. Thelarger phase angles are most likely to occur for plants with greaterseparation and hence with intervening plants, and for these the two-stepequation is closely applicable.

The foregoing two-step loss equation, like the foregoing originalone-step loss and comparison equations and method, is, and is describedin the aforementioned paper as being, an expression which was developedfor use in simplifying the adequate planning of power -system expansion.I have discovered, however, that'this two-.step loss expression orequation constitutes a practically useful and desirable tool for use inautomaticallytdetermin ing deviation from economic balance between theplants of an actual operating system, and in assigning the plant wherein`,loads in such an actual system so as to provide the'most lso Vphaseangle A0.

the two plants are in economic balance.

"6 economical cpibinaton of plant loadings An impoitaxit feature"`ofthetwo-step loss Lequation lin thisconnection is that its use makes itunnecessary for the plants between which economic balance comparisonsare effected to be electrically close together.

In connection with the last mentioned discovery, I have inventedimproved economic load assigning apparatus which operates according tothe foregoing two-step loss method and equation, and hence embodies theforegoing feature. Thus, this improved apparatus can be and desirably isarranged to compare the incremental generating costs and transmissionlosses between one plant, chosen as the lreference plant, and each otherplant of the system. In other words, the use of the foregoing two-steploss equation in this apparatus permits each generating plant in thesystem to be compared directly with a single chosen reference plant,since the greater distances between comparedv plants resulting from thiscomparison method do not produce consequentialinaccuracies when thetwostep loss equation is'employed.

' This'improved economic load assigning apparatus, constrncted andarranged to operate in accordance with the foregoing two-step lossequation and hence in accordance withthe desirable directplants-to-reference plant economic balance comparison method justdescribed, operates with improved accuracy and flexibility, and with asmaller amount of equipment, in comparison to the apparatus of myaforementioned copending application. Therefore, it is apparent thatthis improved apparatus represents a practical and significant advanceover the apparatus of said copending application. This improvedapparatus is disclosed and claimed in a second copending applicatiol1`of mine VSerial No. 632,839, liled oneven date herewith.

I have also discovered, moreover, and have disclosed 'and claimed in thelast mentioned application, an improved, novel comparison method fordetermining when the two plants iof a pair are in economic balance andhence have equal incremental cost and loss ratios and equal incrementalcosts of delivered energy, for detecting deviation fromeconomic balancebetween such plants', and for use in assigning the loads to the plantsin accordance with their incremental costs of delivered energy. Thisimproved comparison method is characterized by the use of an incrementaltransmission loss ratio which isy a predetermined linear function ofthecorresponding Specifically, in accordance with this improved comparisonmethod, an incremental transmission loss ratio for Vtwo plants, whichisa predetermined linear function of the phase angle 0 for the twoplants, is compared to an incremental generating cost ratio for the twoplants which is equal'to the incremental transmission loss ratio whenAny deviation or difference between these Aratios represents avcorresponding deviation from economic balance between the two plants,and a corresponding deviation fromequal increment'al costs of deliveredenergy for the two plants.

In connection with the foregoing novel comparison method, Ihavedeveloped, and have disclosed in the last mentioned application, a noveleconomic balance or comparison expression or equation which is based onthe foregoing two-step loss equation and in which the incrementaltransmission loss ratio term is a linear function of', while thelincremental generating cost ratio term is selected and arranged to beequal to the loss ratio term whenthe two plants involved have equalincremental de- `livered,energy costs at any given point and are ineconomic balance.v This novel linear two-step balance equation isi and 6are the foregoing respective constant ratio and bus voltage phase anglefor the two plants.

Equation l is obtained by rearranging the basic economic balanceEquation 11 of my aforementioned paper,

and by combining this new basic balance equation with the foregoingtwo-step incremental transmission loss equation of column 5, line 32:

dL 4K tan it@ (iP-(K-I-tan lis? By assigning a series of values to inthe right-hand or loss ratio term of the foregoing improved balanceEquation 1, and by then plotting a series of curves of the value of theloss ratio term versus 0, each curve being for a different arbitrarilyassigned value of K, it is seen that this loss ratio term isa linearfunction of 6, as is desired. Specifically, it is shown by such plottedcurves that this loss ratio term can be expressed as follows:

Since the right-hand term of Equation 2 is clearly a linear expressionor function of 0 for any given value of the constant K, it is apparentthat the incremental transmission loss ratio term of the above balanceEquation 1 is a linear function of 6.

Accordingly, the above two-step linear balance Equation 1 can bewritten:

Thus, when the value of the left-hand, incremental gen erating costratio term of Equation 3 is equal to the incremental transmission lossratio value expressed by the right-hand term as a linear function of 6,Equation 3 is satisfied, and the two plants involved have the sameincremental cost of delivered energy at any given point, and hence arein econo-mic balance.

In addition to discovering the foregoing novel linear comparison method,I have invented novel apparatus for carrying out this method inaccordance with the foregoing linear balance or comparison Equations land 3. As will be apparent, this new apparatus represents a practicaland significant improvement over the apparatus of my first mentionedcopending application, since the irnproved apparatus provides improvedaccuracy and exibility of operation while being appreciably less complexthan that of said first mentioned copending application. This improvedapparatus is disclosed and claimed in the second of my above-notedcopending applications.

ln addition to the foregoing, I have discovered an improved and noveleconomic balance determining and plant load assigning method which I amdisclosing and claiming herein as the improved method of the presentinvention, and which is characterized by the foregoing objects. Thisimproved method is based on the foregoing linear two-sten balanceEquations 1 and 3, but represents a significant and practicalimprovement over the foregoing method.

Specifically, the improved method of the present invention is based on adiscovery which I have made that the economic balance and relativeincremental delivered energy cost determinations for the plants of asystem can be effected by comparing each plant with a predeterminedreference point on the system which is common to all of the plants andwhich is not necessarily a generating plant. This discovery alsoembodies the novel concept that such comparisons and determinations bemade at the respective plants. In this connection, I have discoveredthat the plant loads or outputs can be advantageously assigned in aneconomic manner at the respective plants on the basis of the relativeincremental delivered energy cost and economic balance computations andcomparisons effected at the plants themselves. One of the manyadvantages of this improved method is the resulting elimination Vof theneed for telemetering data back and forth between each plant and acentral location, as is required in the performance of my previous loadassigning methods. More specifically, I have discovered that theforegoing economic balance Equation 3 can be rewritten as a new economicbalance or comparison equation for comparing any generating plant with afixed and arbitrary value of generating cost at the aforementionedchosen common point on the system. This new equation is:

wherein: alF/al1n is the incremental generating cost for plant n, Fo isthe arbitrary reference generating cost for the common reference point0,0 o is the phase angle in degrees by which the bus voltage at Plant nleads the reference voltage at point o, and K is the constant ratio ofthe reactance to the resistance of the equivalent path or transferimpedance between Plant n and point o.

It will be remembered that Equation 3 is employed to determine when theplants of a pair are in economic balance, since this equation issatisfied only when the incremental delivered energy costs of thecompared plants are equal, and hence when the plants are in economicbalance. Similarly, the new balance Equation 4 is employed in accordancewith the present invention to determine when the corresponding plant isin economic balance with respect to said common point, since this newequation is satisfied only when the incremental delivered energy costfor the corresponding plant is equal to the incremental delivered energycost common to the other plants at the time, and hence when thecorresponding plant is in economic balance with the other plants.

Finally, in connection with the foregoing improved method, I haveinvented improved and novel economic balance determining and plant loadassigning apparatus which I am disclosing and claiming herein as theimproved apparatus of the present invention. This apparatus ischaracterized by the foregoing objects of the present invention, andrepresents a significant and practical improvement over the apparatusand arrangements of my aforementioned copending applications. Of themany practical advantages provided by this improved apparatus, one ofespecial importance is the material reduction in the number oftelemetering channels required as compared with the number needed whenthe arrangements of my aforementioned copending applications areemployed.

'In accordance with the foregoing, it is an object of the presentinvention to provide a novel method and apparatus as just describedwhereby an economic balance determination is effected at each ofselected ones of the system plants Vby means of computing, comparing,and economic balance deviation detecting apparatus located at thecorresponding plant and operating, in accordance with "the improvedeconomic balance Equation 4, and hence in accordance with my improvedeconomic balance comparison method and my novel yphase angle method ofincremental transmission loss determination, to provide an effect whichis representative of any departure of the incremental delivered energycost for the corresponding plant from equality with the incrementaldelivered energy cost which is then common to the others of the plants,and whereby the effect so derived at each plant is utilized at the plantas a measure of the load change to be assigned to the plant in Order toreestablish equality be tween the incremental delivered energy co-stsvfor the plants, and hence to cause the plants to be loaded in the mosteconomical manner.

The. foregoing and other desirable objects of the present invention arefulfilled by providing at each system plant, in accordance with theinvenlion, a computing and comparing arrangement for determining whenthe corresponding plant is in economic balance with the others of theplants, for detecting any deviation from such balance, and for derivingand 4producing an effect or signal which is representative of or ameasure of any such deviation or departure from balance, and which isalso a measure of the amount and direction by which the plant outputmust be changed in order to return the plant to a state of economicbalance with the other plants. ment at each plant operates to derive andproduce a first effect or signal which is representative of or a measureof the existing incremental transmission loss for the correspondingplantl with respect to a chosen reference point in the system which iscommon -to all of said plants. Said arrangement also derives andproduces at its plant a second effect or signal which is a measure ofthe existing incremental generating cost for that plant `Jvith respectto said common point, lsaid first and second effects being equal whenthe corresponding plant is in economic halance. Finally, saidarrangement compares said first and second effects and produces itseconomic balance deviation effect or signal upon the detection ofinequality between said eifects.

In providing the foregoing operation, each of said arrangementsaccording to the invention produces at its corresponding plant as saidfirst or loss effect a signal which is proportional in magnitude to theactual value for that plant of the right-hand or incrementaltransmission loss ratio term of balance Equation 4. This value ascornputed is thus a linear function of the value of the phase angle 0between the bus voltage of the corresponding plant (Plant n) and thereference voltage at the reference point o. To this end, a single commonmaster reference voltage signal is supplied lto all of the plants, thissignal having a phase which is the same at all plants and which isrepresentative of the phase of the reference voltage at point o. A phasecomparison is effected between this signal and the plant bus voltage todetermine the value of 0 0 The phase angle 0 0 at Leach plant is thusthe phase angle between the plant bus voltage and the reference signal,and is specifically the angle in degrees by which the plant bus voltageleads the reference signal.

The second or cost effect produced at each plant is a signal which isproportional in magnitude to the actual value for the correspondingplant of the left-hand or incremental generating cost ratio term of'balance Equation 4. When any plant is not in economic balance withrespect to the reference point, and hence with respect to the otherplants, the incremental generating cost signal does not equal theincremental transmission loss signal for the plant, Equation 4 is notsatisfied, and the foregoing deviation signal is produced, having amagnitude and sense which are respectively dependent upon the extent anddirection of plant unbalance. This magnitude and sense are alsorespectively representative of the extent and direction of departure ofthe incremental delivered energy cost for the plant from .a common valuefor all of the plants representing the most economical plant loadings.

Finally, said magnitude and sense of the deviation signal arepresentative of the respective amount and direction by which the plantoutput must be changed in order to restore the plant to the 'balancedcondition, malte the plant loss and cost signals equal, satisfy Equation4, reduce the deviation signal to Zero, canse the plant to operate atthe same incremental cost of delivered energy as the rest of the plants,and cause the system to operate in the most economical manner.

The deviation signal produced at each plant is utilized as a basis forassigning the `load to the plant in accordance with its incremental costof delivered energy, or,

,more specificallyl for effecting :the change in the plant Output.necessary to restore the plant to economic balance.

This arrange- 10 Such load assignment or load change may be effectedmanually in response to an indication produced by the deviation signal,or may be effected automatically by the deviation signal. In eithercase, the output of the plant is changed in accordance with thedeviation signal in the direction and to the extent necessary to reducethis Isignal to zero.

For the purpose of controlling the plant outputs as dictated by therequirements of the system, provisions are made, according to theinvention, for varying the phase of the reference signal in accordancewith the deviation, if any, between the actual and desired operatingconditions of the system, or, in other words, in accordance with thedeviation of the existing values of the system conditions from thescheduled values of these conditions. Such changes made to the commonphase of the reference signal cause the plant balance deviation signalsto change correspondingly and to reect the schedule deviations. Thisresults in plant output changes which correct for and eliminate theschedule deviations, these changes being made in such a manner that thenew values of plant loads represent the most economical combination ofplant loadings for the new system condition values.

Accordingly, the common reference signal sent to all plants can be madeto effect the changes in the plant outputs necessary to eliminate systemschedule deviations, while at the same time maintaining the mosteconomical distribution of the system load among the plants. Thus, thisreference signal serves to control the plant outputs as necessary tomaintain the scheduled Values of the system conditions, in addition tovserving to coordinate the economic balance comparisons made at theplants and controlling the plant outputs so as to provide the mosteconomical combination of plant loadings for the existing systemsconditions.

In accordance with a further aspect of the present invention, means maybe included at one or more of the foregoing plants for determining andproviding at that plant an effect or indication of the equivalentgenerating cost at some `other location in the system relative to thearbitrary reference generating cost for the reference point o. Suchmeans may be employed for the purpose of providing, at the plantincluding it, an indication of the incremental value of energy at saidlocation, ywhich location may well kbe an interconnection point betweenthe system and that of another area or company. In some cases, saidmeans may serve a correcting function at .the plant including it, thecorrection obtained being one which may be desirable for the case wheresaid location is a predetermined system :point which -is electricallylocated between the plant in question and the reference point, and wherethere is a substantial difference between the reactance-resistanceratios `of the transfer impedances between the plant and saidpredetermined point, and between said predetermined point and thereference point.

A better understanding of the present invention may be had from thefollowing detailed description of appa- `ratus embodying the invention,which description is lto be read in connection with the accompanyingdrawings, wherein:

Fig. 1 is a block diagram showing a typical application of thepresentinvention to a typical electric power generation and distributionsystem;

Fig. 2 is a schematic circuit diagram of a form according to theinvention which the economic balance computing, comparing, and loadassigning apparatus at each of the Fig. 1 system plants may take;

Fig. 3 is a schematic circuitfdiagram of a form according yto theinvention which the common reference signal producing apparatus at thedispatchers location of the Fig. 1 arrangement may take;

Fig. Al is a schematic circuit diagram of a modification of a portion ofthe Fig. I2 apparatus embodying the invention and useful in certaincases; .and`

yPlant No. 3.

THE ARRANGEMENT OF FIG. 1

The block diagram of Fig. l illustrates broadly a typical electric powergeneration and distribution system which is under the control ofautomatic economic load assigning apparatus according to the presentinvention. The system of Fig. l is shown, by way of example, as havingthree generating plants whose outputs are under the control of theapparatus of the invention. It is to be borne in mind, however, that themethod and apparatus of the invention are applicable to systems havingany number of generating plants, and to systems having certain selectedplants under the control of the apparatus of the invention and havingother plants which, for one or another reason, are not subject to theeconomic load assigning operation provided by this apparatus. Also, themethod and apparatus of the invention are applicable to systems whereinthe outputs of certain of the system plants are controlled automaticallyby the apparatus of the invention while the outputs of certain of othersof the system plants are controlled manually in accordance withinformation provided by the apparatus. Moreover, the invention isapplicable to Systems wherein all of the plants are under automaticcontrol or are under manual control.

However, for simplicity of description and explanation, it will beassumed herein that the system of Fig. 1 includes only the illustratedthree generating plants, and that all of these plants have their outputsor generation assigned or controlled in an optimum economic manner byapparatus according to and embodying the present invention. Thus, theloads are assigned to the three plants of the Fig. 1 system by saidapparatus in accordance with the incremental costs of delivered energyfor the plants so as to coordinate the incremental transmission lossesand incremental generating costs in the system to the end of securingthe most economical combination of loadings for the three plants, andthe most economical operation of the system, under the existing systemconditions.

The three plants of the sysetm shown in Fig. 1 have been designated inFig. l as Plant No. l, Plant No. 2, and The system also includes adispatchers location or dispatching oice generally designated by therectangle identified by the numeral 1. The remainder of the system isgenerally designated by the rectangle bearing the numeral 2, andincludes the system transmission lines, distribution equipment, loads,and all of the other system portions and equipment other than the Plantsl, 2, and 3 and the dispatching oce 1.

Each of Plants 1, 2, and 3 is shown in Fig. 1 as consisting of twoportions, each of which is designated generally by a suitably labelledrectangle. One of these two lportions is a computing and load assigningapparatus portion which is constructed, arranged, and operative inaccordance with the present invention, while the other of the twoportions represents the remainder of the corresponding plant andincludes the plant generators, turbines, boilers, etc. The computing andload assigning apparatus portions for Plants 1, 2, and 3 arerespectively identified by the numerals 3, 4, and 5, while the remainder of each of Plants l, 2, and 3 is designated by a corresponding oneof the numerals 6, 7, and 8.

The respective outputs 9, 1t), and 11 of Plants 1, 2, and 3 are shown asbeing connected to the remainder of the system in the usual manner. Eachof these outputs is controlled or assigned, in accordance with thepresent invention, by means of the corresponding one of the computingand load assigning portions 3, 4, and 5. In

lother words, the magnitude of the output of each plant,

or of the plant load, is determined and assigned at each 12 plant by thecorresponding computing and load assigning apparatus at the plant.

Since the computing and load assigning apparatus 1ocated at each ofPlants l, 2, and 3 is constructed and operative in accordance with thepresent invention, this apparatus assigns the load to the correspondingplant as necessary to maintain the plants in economic balance, to securethe most economical combination of plant loadings, and to provide themost economical operation of the system. Thus, the computing and loadassigning apparatus at each plant is operative to effect such economicloading of the plant in accordance with the novel reference pointcomparison method of the invention as described hereinbefore. To thisend, the computing and load assigning apparatus at each plant issupplied with a irst voltage or signal having the phase of the busvoltage of the corresponding plant, and with a second signal having thereference phase of the voltage at the common chosen reference point ofthe system. Said lirst or plant bus voltage phase signal for each ofPlants l, 2, and 3 is supplied to the respective one of the portions 3,4, and 5, from the respective one of the plant outputs 9, 10, and 11,over a corresponding one of paths 12, 13, and 14. The second orreference phase signal supplied to each of the portions 3, 4 and 5 isthe aforementioned single, cornmon reference signal which is supplied toall of the plants and which has the same phase at all plants. Inaccordance with the invention, this reference phase signal is suppliedto all plants, as by telemetering channels 15, from the dispatchingoffice 1.

It will be remembered that, according to one aspect of the presentinvention, the phase of the common reference signal sent to the systemplants is varied in accordance with the deviation, if any, between thedesired or scheduled system condition values and the actual or existingvalues of these conditions. The purpose of so varying the phase of thecommon reference signal is to permit this Isignal to be utilized as ameans by which the plant outputs can be changed as necessary toeliminate any devia` tions between the actual and desired systemcondition values, or system schedule deviations, while at the same timemaintaining the most economical distribution of the system load amongthe plants.

To the end of providing the operation just described,

the dispatching oflice 1 is supplied with three types of information foruse in producing the common reference signal. Thus, signals representingthe actual values of the system conditions, such as the value of theexisting system frequency and the values of existing tie line loads, aresupplied to the dispatching office l from the necessary points in thesystem, as by means of the illustrated telemetering channel 16. Alsosupplied to the dispatching office 1 is information as to the desired orscheduled values of the system conditions, as shown in Fig. l by thedotted path 17. Finally, a reference voltage is supplied to thedispatching oice 1 by means of the path 18, from which the apparatusincluded in the dispatching office derives the common reference signalon the basis of any deviation between the actual and desired values ofthe system conditions. This reference voltage may be obtained from anyconvenient source of voltage which is in synchronism with the system. Itis desirable that this source provide a supply of reference voltagewhich has a reasonably stable phase.

OPERATION OF THE FIG. l ARRANGEMENT As was noted hereinbefore, thepurpose of equipping the system of Fig. 1 with the illustrated economicload assigning and controlling apparatus according to the presentinvention is to obtain the automatic control of the outputs of Plants 1,2, and 3 of the system as necessary to fulll the load and frequencyrequirements of the system in the most economical manner. In otherwords, it is the purpose of the Fig. 1 load assigning apparatus as awhole to assign to the plant loads or outputs the values necesnannies;

sary to cause the total 4amount of 'generatedp'ower'in the system to-b'ethat necessary `tof meet the existing-needs of the system, and tocausethis totalgenerated power. to be so divided or proportioned among Plants1, 2,.,ancl 3V as. to provide the most economicalcombination of plantloadings, and operation of the system at a minimum-total cost ofdelivered energy, and hence: in the most economical manner.

In achieving the foregoing desired operation and results, each ofthecomputing and load assigning. apparatus portions 3, d, and Sisoperative to assignthe load tothe corresponding plant, or, moreparticularly,.to control the output of the corresponding-plant, asdictated bythe phase of the common reference signal and in accordancewith the existing incremental cost of delivered energy for the plant.One of the objects of this control; isr to maintain the outputs of theplants at the values necessary to cause the plants to operate with.equal incremental costs of delivered energy, and hence to keep theplants in economic balance, for the existing load conditions. The otherobject of this control is to change the plant outputs, upon a change inthe phase or the commo-n reference signal, so as to correct the totalsystem generation as necessary to eliminate the schedule deviationconditionwhich caused the reference signal phase change, while at thesarne time assigning this new total plant output among. the plants inaccordance with their existing relative incremental delivered energycosts to the endof re-establishing equality between these costs `andmaintaining theplants in economic balance for the new operatingconditions.

ln accordance with the foregoing, each; of the comput- -ing and loadassigning portions 3, 4,. and is operative in accordance with theforegoing reference. plant comparison method and economic balanceEquation 4 to determine continuously whether or not thecorrespondingplant is in economic balance with the. chosen` reference point, and toeffect automatically the necessary change in the plant output to returnthe plant to economic balance if the effected economic balancedeterminations indicate that the plant is not in economic balance.Specifically,A each of the portions 3, 4, and 5 computes the incrementaltransmission loss ratio for thecorresponding plant` on the basis of thephase angle between the reference signal and the plant bus voltage, andalso. computes the corresponding incremental generating cost ratio forthe plant on the basis of the plant operating level and the plantoperating cost. The apparatus at each. plant etfectsl a continuouscomparison between these loss and cost ratios according to Equation 4,and detects any economic unbalance between the plant and the referencepoint by detecting Aany deviation between the above loss and costratios. On occurence of such deviation, the apparatus operates inaccordance with this deviation to change the plant output as necessaryto reduce this deviation to zero, to satisfy the balance equation, andto return the plant to economic balance with the reference point. Sincethis operation takes place continuously at all of the three systemplants, whereby each of the plants is controlled to be in economicbalance with the reference point, it is apparent that this operationcauses all of the plants to be in economic balance with each other.

As long as the requirements of the system are met by the existinggeneration supplied by Plants 1, 2, and 3, the phase of thecommonreference signal remains constant. This signal serves at such timeto coordinate the economic balance comparisons effected at each plant bythe corresponding computing and load assigning apparatus at the plant.In other words, the common reference signal under these conditionscorrelates the computations and comparisons made at the plants, since itrepresents, by its identical phase at each plant, the basis or referencepoint value withwhich each` plant is compared in order to determinewhether the plants are in economic balance with each other. As a resultchanges in system load pattern or other system conditions which cause a.

departure from economic balance betweenl the` plants; even though noschedule deviation is produced, result in deviations at the plants frombalance between the plants and the common reference signal. Suchdeviationsv cause the necessary changes to` be effected in the plantloutputs as required to eliminate the deviations and to return each plantto the condition of economic balance with the reference point, and henceto re-establish thev condition of economic balance between all of theplants.

Upon the occurrence of a schedule deviation inthe system, the resultingchange inthe phasel angle of the common reference signal atv each plantcauses thev production of deviation effects between the plants and thereference signal which are not eliminated'until the plant outputs havebeen changedv as necessaryto offset the system conditions producing theschedule deviation, and until the condition of economic balancey hasbeen re.- established between the plants for the new system conditions.

THE APPARATUS OFV FIG. 2

Fig. 2 illustrates the details of apparatus embodying the presentinvention which can be used to advantage as the computing and loadassigning apparatus at each of the plants of the Fig. 1 arrangement.Thus, Fig. 2 illustrates a desirable form which each of the apparatusportions 3, 4, and 5 of Fig. l may take. For purposes of description andexplanation, it will be consider-ed that the computing and loadassigning apparatus of Fig. 2 is the apparatus 3, which is individual toPlant 1.. lt should be noted, however, that eachk of the apparatusportions 4 and 5 of the respective Plants 2 and 3 can alsoadvantageously be of the form of the Fig, 2 apparatus, if desired. Inother words, the apparatus shown in Fig. 2 is suitable for use as any ofthe apparatus portions 3, 4, and 5 shown generally in Fig. 1, but istreated herein as being the apparatus portion 3 for the purpose ofsimplifying the description of the invention.

In Fig. 2, the portion 6 of Plant 1 is shown as including a firstgenerating unit 19 and a second generating unit 20.

While there may be one or more additional generating units at Plant l,only the two units 19. and 20 are shown in Fig. l, this being done forthe purpose of preventing undue .complexity of the drawings anddescription. It is to be noted, however, that the load assigningapparatus 3 to be described, could be arranged to control as manygenerating units in the plant as desired, and that the operation of thisapparatus would be the same for any number of units as it is inconnection with the two units illustrated in Fig. 2. v

The apparatus 3 of Fig. 2 includes a phase angle de termining portion21, a computing, comparing, and generator load controlling portion orsection 22 for generating unit 19, and a section 23 which is identicalto the section 22 but is individual to the generating unit 20. Theapparatus of Fig. 2 would also include an additional section, not shown,for each additional generating unit at Plant 1, each of these additionalsections being identical to the illustrated sections 22 and 23 for units19 and 20 respectively.

The general purpose of the sections 22 and Z3 collectively is to controlthe outputs of the associated generating units 19 and 20, and hence thetotal plant output, as necessary to maintain Plant 1 in economic balancewith respect to the common reference point o, and hence in economicbalance with Plants 2 and 3. To this end, each of the sections 22 and 23is arranged to control the output of its corresponding generating unitto the value which causes the economic balance equation for thatgenerating unit to be satised. This necessitates that each of thesections 22 and 23 be supplied with an effect which is representative ofthe existing value of the phase angle @1 0 between the plant 1 busvoltage and the common reference signal, since the economic balanceequations are functions of this angle, as explained hereinbefore. Thisetfect representative of the existing value of the phase .1, Ki-o-Itacts 34 and 3S of these two resistors are mechanically gangedtogether, and are arranged to be adjusted along;

15 angle @1 0 is supplied to each of the sections 22 and 23 by the phaseangle determining portion 21.

For the purpose of simplifying the following detailed description of thesection 22, this description treats the operation of the section 22 andthel unit 19 controlled thereby as if the output of the unit 19 is theentire output of Plant 1, and as if Plant l is in economic balance aslong as the economic balance equation for unit 19 1n section 22 issatisfied. In other words, the present description of the section 22treats this section as though it and the unit 19 controlled by it makeup the entire Plant 1 Such an approach is proper and accurate, since theoperation of the section 22 represents or portrays the operation of allof the other corresponding sections of the Plant l control equipment,and since the economic balance status of the output of unit 19 is anaccurate representation of the status of the outputs of the other plantunits and of the plant output. The reason for this is that the operationof the other units of Plant l, under the control of their respectivecontrol sections, follows or parallels the operation of the unit 19under the control of the section 22. Accordingly, the operation, output,and economic balance status of any one of these units and sections, suchas the unit 19 and section 22 chosen for illustrative purposes, actuallygive a true and accurate picture of the operation, output, and economicbalance status of the entire Plant l.

The section 22 The specific purpose of the section 22 is to compute theexisting values of the incremental transmission loss and incrementalgenerating cost ratios of Equation 4 associated with the operation ofgenerating unit 19, and to utilize these ratios in determining, inaccordance with Equation 4, whether or not generating unit 19, and hencePlant 1, are operating in economic balance with respect to the othergenerating units at Plant l, the common reference point, and theremaining Plant 2 and 3 of the system, section 22 is also arranged toassign or control the output of generating unit 19 as necessary tomaintain equality between the corresponding loss and cost ratios, andhence as necessary to maintain the economic balance comparison equationsatisfied for generating unit 19, to the end of maintaining Plant l ineconomic balance with Plants 2 and 3. l

In accordance with the foregoing, the section 22 includes a computingand comparing bridge circuit having input or energizing terminals 24 and25, and having output terminals 26 and 27. A first adjustable resistor28, the body of a slide wire resistor 29, and a second adjustableresistor 30 are connected in series in the order stated in a rst branch'between the energizing terminals 24 and 25. The adjustable Contact 31of the slide wire resistor 29 is connected to the bridge output terminal26.

Adjustable resistors 32 and 33 are connected in series 'in a secondbranch between the energizing terminals 24 Loss ratio computation Thepurpose of the first or upper branch of the bridge circuit of section2.2 is to compute the existing value of the incremental transmissionloss ratio of Equation 4 for section 22, and to produce a potential orsignal which is proportional in magnitude to this value. To this end,the adjustable resistors 2S and 30 of the bridge circuit `are employedfor introducing into the bridge circuit, and

the computations made thereby, the existing numerical value of theconstant reactance-rcsistance ratio for Plant For this purpose, therespective adjustable con` their respective resistors to a positionrepresentative ofthe existing value of K1 0. Specifically, the contacts34 and 35 are arranged to be manually positioned through a suitablemechanical linkage 36 by means of knob 37. A scale and pointerarrangement cooperating with the knob 37 facilitates the proper manualadjustment of the eiective resistances of the resistors 28 and 30 inaccordance with the numerical value of the constant K1 0, in a mannerwhich is described in detail hereinafter.

The slide wire resistor 29 is employed for introducing into the bridgecircuit, and the computations which it effects, the existing numericalvalue of the phase angle @1 0 between the bus voltage of Plant 1 and thereference voltage. To this end, the contact 31 is arranged to bepositioned along the slide wire 29 in accordance with this phase anglevalue. This is done by means of a suitable mechanical linkage 38 whichis actuated by the phase angle determining portion 21, to be describedhereinafter. It is suhcient to note at this point that the slide wire 29is a so-called zero center device, and that the portion 21 positions thecontact 31 on the slide wire Z9 to the right of the zero position whenthe plant bus voltage leads the reference signal and @1 0 is thuspositive and positions the contact 31 to the left of the zero positionwhen the bus voltage lags the reference signal and @1 0 is thusnegative. Moreover, the portion Z1 so positions the contact 31 on theslide wire 29 that the distance of the contact from the zero centerposition at any time is a measure of the existing value in electricaldegrees of the phase angle @1 0. Therefore, the posi tion of the contact31 on the slide wire 29 is a measure of both the magnitude and sense orsign of the existing` phase angle @1 0.

By virtue of the foregoing, the upper bridge branch including the Kresistors 28 and 30 and the phase angle slide wire 29 computes andprovides the eiect or signal which is proportional in magnitude to theexisting numerical value of the right-hand, incremental transmissionloss ratio term of balance comparison Equation 4. As noted hereinbefore,the magnitude of this loss signal is a function of solely K1 0 and @1 0,being a linear function of @1 0. This loss signal appears on the contact31, and hence on the bridge output terminal 25, and is of a value, withrespect to a point midway in potential between the bridge energizingterminals 24 and 25, which is proportional to the existing numericalvalue of the loss ratio term of Equation 4.

Cost ratio computation The second or lower branch of the bridge circuitof section 22, containing the adjustable resistors 32 and 33, isprovided for the purpose of computing the existing value of theincremental generating cost ratio of Equation 4 for section 22, thiscast ratio being equal in value to the foregoing loss ratio when unit19, and hence Plant 1, are in economic balance with respect to thereference point o and the Plants 2 and 3. Also, the purpose of thislower bridge branch is to produce a potential or signal which isproportional in magnitude to the value of this cost ratio, which isequal to the value of the above described loss signal when economicbalance conditions for Plant l exist,'and which is arranged to becompared with said loss signal in order to detect any economic unbalancefor Plant l.

To this end, the adjustable resistor 32 is employed for introducing intothe bridge circuit, and the computations 3 arbitrary generating cost F0for the reference point o.

17 The speciic manner in which .this adjustment may d esiraoly be made'in practice will be set forth in detail hereinafter.

The adjustable resistor '33 is employed for introducing into the bridgecircuit and its computations the value of the incremental generatingcost dF/dP for the generating unit 1'9. Thus, the effective resistancevalue of the resistor 33 is arranged and controlled to .be proportional'to Vthe value of this incremental generating cost. This Yrequires thatthe resistance of the resistor .33 be proporti'oned Ain accordance with`a design value for the price 'or 'costof fuel at Plant yLandth'at theeiective resistance 'of the `resistor 33 be 'adjusted Yin `accordancekwith the 'output'of theunit :19, or, more specifically, in accordancewith the incremental input'o't'co-st required to produce an kincrementaloutput 'of power at the existing output of 'the unit 19at`any giventime.

Thef'orego-ing Vis accomplished 'in lthe Fig. 2 apparatus by "means 'ofa cam land 'follower combination 42--43 which positions an 'adjustablecontact 44 along the refs'istor 33 through a'su'itable mechanicallinkage 45. The cam 42 Iis shaped in 'accordance with the boiler-turbineinput-output characteristic lfor the unit 19, and is arranged fto ibelpositioned by the turbine valve shaft of the turbine of 'the -unit 19.This causes the contact 44 'to be `positioned on the resistor 33 inaccordance with 'the outputfof fthe unit 19, and, mo-re specifically, inac- VAPlant .1 from the cost'assumed in proportioning the re- Ss'istor33, and'for 'changes which affect the yoperating efticiencyof the unit:19 and its associated equipment, and hence cause the unit tooperatewith a different characteristicrfrom that oniwhich'the design of the cam42 was based.

Iffdesiredythe"positioning of the contactf44 in accordfaneei'withtheoutput ofthe unit 19 can be arranged to be effected by other than theturbine valve shaft as illustratedby'way of example in Fig. 2. Thus,if'desired, fthe cam 42 can be arranged to be positioned by meansldirectly responsivev to the actual unit output. Further, by employingas the resistor 33 a resistor which is characterized rin accordance`with the desired input-output characteristic, the need for lthe cam andfollower arrangement 42-43 is eliminated. Such a resistor may be woundto have the .desired characteristic, or-may well be ofthe -known typewherein the characterization is ad- ;justable bysuitable means.

By virtue Iof the foregoing, the lower bridge branch vincluding theresistors 32 and 33 computes and provides .theetfect or signal which isproportional in magnitude to the existing value of the left-hand,incremental generating cost ratio term of Equation 4 for section 22.This cost signal appears at`the`bridge output terminal 2'7, and is of avalue, with respect to apoint midway in potential between the bridgeenergizing terminals 24 and 25, which is proportional to the existingnumerical value of the cost ratio term of Equation 4. This cost signalis equal in Value to the foregoing loss signal when economic balanceconditions exist-for unit 19 and Plant 1, at which time there is nopotential difference between the bridge output terminals 26 and`27.

`Balance deviation detection and load control As was "previously noted,the section 22 eiects a continuous comparison between the foregoingincremental *transmission loss and generating cost ratio signals so as`to .detect any deviation between `these signals, and hence anydeviation between the corresponding cost and loss ratios, any suchdeviation lit-ing representative of a deviation from economic balancefor Plant 1. This signal comparison is etectedby comparing the signalsor potentiais produced'on the bridge output terminals 26 and 27, or,more specifically, by comparing the potential .-of `the terminal 26 withvthat of the terminal 27. This amounts to detecting the Lvpotentialdifference orpotential, if any, .produced between the terminals 26 and27. The value of this potential or deviation signal is Yzero Y'as longyas the loss and cost signals and ratiosare equal, andhence .as long asPlant l is in economic balance.

For the purpose of effecting this economic balance comparison or thisdetection of the ypotentialor deviation signal between `the bridgeoutput terminals 2v6and 27, a suitable potential responsive device 46,shown asfa zero-.center galvanometer, is connected in series with acondenser 47 between `the terminals 26 and 27. A first resistor 4% is'connected across the `galvanometer 46,.and a second resistor 49isconnected across the condenser 47. The condenser 47 and the resistors48 and 49 impart a rateresponse or rate action to the galvanometer 46which will be ,described hereinafter. y

By virtue ofthe foregoing connections, thegalvanometer 46 detects, andis responsive to, the appearance 4of the foregoing deviation signalbetween the bridge .outyput terminals 26 and 27. ,The resulting deectionof the `galvanometer pointer is anindication of the departure of unit 19andPiant l Afrom economie balance, and 4is utilized vfor assigning theload to unit 19 or, more speciically, for controlling the output of unit19, as necessary yto return this output toa value whichprovideseconomic(balance for unit i9 and Plant l.

To this end, the galvanometer 46 is arranged to Control the output ofunit 19 andof Plant vl as necessary to maintain zeropotential-difference between the bridge outputterminalsl and 27, andhence as necessarylto maintain the loss and cost signals and ratiosequal, the balance comparison equation satisfied, the bridge circuitbalanced, and the Plant 1 in economic balance. Thus, the galvanometer 46is advantageously of the wellknown proportional controlling type, and isarranged to kcontro-1 the operation of a reversible, governor .setpointadjustingmotor /Stl'or the governor of the unit 19. `Spe citically,'the vgalvanometer 46 controls the operation of themotor 5t) through theusual relay Si, which is connected :between the galvanometer 46 and themotor 50 by suitable conductors 52, The motor Si) .adjusts the 'setpoint of the governor of unit 19 through a suitable mechanical linkage53.

In the usual manner Jfor such a lcombination of a proportionalcontrolling galvanometer anda reversible motor, the motor Si) is causedto rotate in one direction when the galvanometer 46 detects a potentialdifference 'of onepolarity between its terminals and hence deects sitsVpointer in one direction away from the zero center position. Similarly,the motor 50 is caused to rotate in the opposite direction when thegalvanometer 46 detects apportential diference of the opposite polarityandhence vdeilects its pointer from zero in vthe opposite direction. lnboth cases, the speedof rotation of the motor 50, .and hence the rateofchange oradjustment of the governor setpoint, is proportional to theextent of the deection ofthe galvanometer pointer `from-the zero centerposition, and to thel magnitude of the potential across thegalvanometer. When thereis noV potential across the gal- 'vanometer 46,the motor S0 isnot actuated for rotation in either direction, wherebythe governor set pointthus remains in the position into which it waslast adjusted by the motor 50.

Since Itheconstruction and operation of-such a proportional controllinggalvanometer operating a reversible motor is well known, no furtherdescription of the de Operation of the section 22 When, and as long as,the operation or output of the generating unit 19 is such that thisunit, and Plant 1, operate in economic balance with respect to thereference point and the other system plants, the economic balanceEquation 4 for unit 19 is satised. This means that, under thiscondition, the incremental transmission loss and incremental generatingcost ratios and signals for unit 19 are equal, and that there is thus nopotential between the bridge output terminals 26 and 27. In other words,the presence of zero potential between the bridge output terminals is anindication that the output of unit 19 is that required to maintain Plantl in economic balance for the existing system conditions.

Under this condition, the pointer of the galvanometer 46 rests at thezero-center position, since there is no bridge output or economicbalance deviation potential or signal to be detected at this time. Thus,the governor adjusting motor 50 is not actuated, and the output of unit19 is not adjusted or changed, but continues at the value producing theeconomic balance condition.

A departure from economic balance for unit 19 and Plant l, due to one oranother cause, means that the existing output of unit 19 is no longerthat required to produce and secure such economic balance. Upon theoccurrence of such a departure, there is a departure from equalitybetween the cost and loss ratios for unit 19, whereby balance Equation 4is no longer satisfied. This results in a departure from equalitybetween the cost and loss signals in the bridge circuit, and in theappearance of the deviation potential or signal between the bridgeoutput terminals 26 and 27. Thus, the appearance of this deviationsignal is an indication that unit 19 and Plant l are no longerineconomic balance, or, in other words, that there is a deviation fromsuch balance.

(l). The extent and direction of deviation from economic balance betweenPlant l and the reference point.

The deViation-from-balance signal which is produced between the bridgeoutput terminals 26 and 27 under the presently described condition ofdeparture from economic balance is of a magnitude and polarity which arerespectively representative of each of the following:

(1) The extent and direction of deviation from economic balance betweenPlant l and the reference point.

(2) The amount and directionof the difference between the incrementalcosts of delivered energy for Plant 1 and the reference point.

(3) The extent and direction of the departure from the rnost economicloading for Plant 1 with respect to the reference point.

(4) The approximate amount and direction by which the output of unit 19,and hence the output of Plant 1, should be changed in order to returnPlant 1 to economic balance and operation with an incremental deliveredenergy cost equal to a common minimum value for all of the systemplants.

Thus, a value of other than zero for the deviation signal producedbetween the bridge output terminals 26 and 27 indicates a deviation ordeparture from economic balance for Plant l, and indicates the need foradjustment of the output of unit 19 and Plant 1 in order to obtain themost economical loading of the unit and plant, and a condition ofeconomic balance therefor.

The appearance of the deviation signal between the bridge outputterminals 26 and 27 is thus indicative of the need for a change in theoutput of unit 19 in order to restore economic balance. Briey, thissignal, and hence the deviation from balance responsible for it, aredetected by the galvanometer 46, which produces a pointer deflection ofa magnitude and direction which are or direction of the deviation signaland the departure from economic balance. This deiiection of thegalvanometer pointer actuates the governor set point adjusting motor 50for rotation in the corresponding direction, this direction being thatwhich causes the resulting change in the set point of the unit 19governor to change the output of the unit in the direction necessary toreturn the unit and plant to the balanced condition.

More speciiically, the presence of the aforementioned rate actioncondenser 47 and the resistors 48 and 49 associated with thegalvanometer 46 cause the deviation signal to produce across thegalvanometer 46 a potential which is proportional in magnitude to boththe magnitude and the rate of change of the deviation signal, and whichhas a polarity corresponding to that of the deviation signal. pointerdeiiection in the corresponding direction is proportional to themagnitude of the potential across the galvanometer, the galvanometerpointer is actually deiiected from zero by an amount which isproportional to both the magnitude and rate of change of the deviationsignal. Thus, the speed or rate at which the motor 50 positions oradjusts the set point of the governor for unit 19 is proportional toboth the magnitude and rate of change of the deviation signal, and henceis proportional to both the extent and rate of change of deviation fromeconomic balance, since the speed of rotation of the motor 50 isproportional to the amount or extent of deliection of the galvanometerpointer from zero.

It is noted that, if desired, the means for controlling the directionand speed of rotation of the governor motor 50 in accordance with thepolarity, magnitude, and rate of change of the deviation signal may beof forms other than the proportional controlling and rate responsivegalvanometer arrangement shown herein by way of example. Thus, thismeans could well be of the form of any of the known so-calledproportional plus reset controllers which are available on the market.Also, if desired, other means, such as pneumatic or hydraulic motors,could be used in place of the motor 50 to control the governor or theoutput of unit 19. Control apparatus applying generation or outputraising and lowering impulses to the governor could also be employed, ifdesired. The particular type of control equipment to be used for anygiven situation depends on the factors and conditions particular to thatsituation.

As is readily apparent from the foregoing, the section 22 assigns orcontrols the output of generating unit 19 in accordance with a measureof the extent and direction of deviation from economic balance for unit19 and Plant l, and of the extent and direction of deviation fromequality between the incremental costs of delivered energy for thesystems plants. This assignment or control of the generation of unit 19is performed as necessary to maintain equality between the cost and lossratios for unit 19, to maintain the economic balance equation for thisunit satisfied, to maintain Plant 1 in economic balance with the othersystem plants, and to maintain equality between the incremental costs ofdelivered energy for the plants.

The Section 23 As was noted previously herein, the section 23 isidentical to the section 22 as just described, but is individual to thegenerating unit 20 at Plant 1. Accordingly, the section 23 is arrangedand operative to control the output of generating unit 20 to the end ofmaintaining the operation of this unit in the manner necessary to keepPlant 1 in economic balance with the other system plants. Thisyoperation is identical to that described above in connection withoperation and control of the section 21 and the unit 19. Therefore, itis suicient to note with respect to the section 23 that the latterincludes components and connections which are identical to thecorresponding components and connections included in Accordingly, sincethe extent of galvanometer the section 22, and that these items in thesection 23 l`bea1 reference characters which Vare the same as thoseapplied to the corresponding items in the section v'22 except for beingin the two-hundreds series.

It is noted in connection with the section 23 that the K resistorcontacts 234 an-d 235 thereof are advantageously arranged to be adjustedalong their respective resistors 228 and 230 by the linkage 31.Acco-rdingly, these contacts are adjusted simultaneously withtheadjustment of the corresponding K contacts in section 22 as thecommon K1;o knob 37 .is-rotated.V Also, the linkage 36 is --shown asextending downwardly in Fig. 2 so as to be available to yposition theKresistor contacts in the additional computer circuits `or ysectionsincluded for controlling any otherv generating units at `Plant `l.` Suchuse of `a common adjusting means for all of the K resistors at Plant 1is permissible because of the fact that the numerical value of K1=ofis=aconstant pertaining to the entire plant and is the -samefor all sectionsand generating units `at the plant.

'fIt isalso notedin connection with the section 23 that the -phase angleslide wire resistor contact 231 thereof vis advantageously -arranged tobe adjusted along the re- `sistor 229 `by the linkage 38, whereby thiscontact is adljusted bythe phase angle determining portion 21simultaneously-with the adjustment of the corresponding con- `tact 31 inthe section 22. Also, the linkage 38 is shown :as extending downwardlyin Fig. 2 so as to be available ito position the phase angle 'resistorcontacts in the control section. for any additional units 'at Plant l.The use of asingle-meansforeiecting'the simultaneous andidentical'adjustmentofall ofthe phase angle resistor contacts at Plant`l is .permissible because of the fact that the numerical value o'f y0111 is the'same at any given time for all of the sections and'units atPlant l.

lThe portion 21 meansof'the common 'mechanical linkage38. Ihe manner inwhich this linkageis actuated to rso'adjust the phase angleresistor-contacts will now be described.

`The portion 21 includes a telemetering receiver 54, a phaseanglemeasuring or determining device 55, and a servo arrangment including afollow-up 'circuit S6, an famplier 57, and a follow-up motor 58. Thereceiver 54 receives'th'e common reference signal which istelemeteredlto Plant l'from the vdispatching oiiice i of Fig. l, and converts thistelemetered signal into the reference phase signal for use at Plant ll.This signal has a phase which is the same as thatlof the referencesignal at each of the other Vsystem plants, and which represents thereference phase of the voltage yat the common reference 'point o.

The phase of tthe reference signal produced bythe receiver 54 iscompared with the phase of the 'Plant l bus vol-tage by the device 55,the output of which is a D. C. signal having a magnitude and polaritywhich are respectively dependent upon the magnitude in electricaldegrees and the sign of the phase angle @1 0 by which the plant busvoltage leads the reference signal. This output of the device 55 isconverted by the servo elements "56, S7, and 58 intoy a proportionalposition which is transmitted by the linkage 38 to each of the phaseangle resistor contacts, whereby each of these contacts is accuratelypositioned in accordance with the value and sign Of @1 0.

Specitically, `the signal ofreference phaseirom .the output terminals 5gof the receiver 54 is applied by 'a pair of conductors 60 vtothetermnals-6ll of one of the inputs of the phase. measuring device 55. Theconductors 12 appty the signal of the phase of the plant bus voltage 'tovthe terminals 62 of the other input of thedevice 55. The D. C. outputsignal from theoutput terminals 63 of the device 55 'isconnected inseries with an 'adjustable D. C. 'output'fro'm th'e `follow-up circuit56 to the -input terminals 64 of the servo amplifier 57. This latter 'isaccomplished oy means of aconductor-TGS which connects one of the outputterminals 63 to one of the inpu't'terminals 64, a vconductor `66 which'connects vth'efother ofthe l output terminals 63 to one 'of the outputterminals 67 l'of the circuit 56, and a Aconductor 68 which connects theother output terminal or slide `wire contacts 69 'of fth'e circuit 56 tothe otherof the `input terminals '64.

The output terminals 70 of `the amplifier -57 fare connected byconductors 71 to the 'motor 158, 'whic'h in turn is arranged to-adjustthe output ofthe circuit'56 bypositioning its contact 69 throughthelinkage 38. The motor SS positions the servo contact 69'in the "mannernecessary to maintain zero input to the amplifier 57, which results inthe positioning of this contact in accordance with the value and sign of01,0. Accordingly, the phase angle resistorcontacts 31 and 231 arelikewise positioned by the motor SS-and the linkage 3S in accordancewith the value'and sign of '01 11.

The phase measuring device :5S maybe of 'anyof the well known 'forms-ofthis 4typeof device which are'available on the market. Sincetheiconst'ruction Vand operation of such devices is well known, -no lfurther reference to the device 55 is seen to be necessary herein.

The servo arrangement including the Aelements '56, .517, and 58 may alsobe of any of the well known forms of such apparatus which are availableon the market, and may well be of the type disclosed in the Wills PatentNo. 2,423,540. Since the manner in which such servo arrangementsareconstructed and are operative toposition a contact, such as thecontact 69, in accordance with the magnitude and polarity of a D. C.signal, such as the output of the device 5S, is well known, no furtherdescription of the present servo arrangement is seen to be necessaryherein.-

It is noted that Vthe phase angle determining portion 21 need not be ofthe specic form illustrated by way of example in Fig. 2, but instead maybe of any suitable desired formwhich will efectthe positioning ofthephase angle resistor contacts 31 vand 231`in`the specified manner. Thespeciiic form chosen for the 'portion 21 for'any given situatie-n willdepend upon'the conditions particular to thatsituation.

It is assumed in connectionwith the showing of the Plant l equipment ofFig. 2 that the line Vconnections to this plant are such 'that a'singlephase angle @1 0 and a single reactance-resistance ratio K1 -0are applicableto all of the generating units in the plant. If, however,Plant 1 were to have a split bus supplyingtwo or more distinctlydifferent lines, and if there were a substantial difference between thephase angles of the voltages of two different sections of the plant busrelative to the reference signal, a separate phase angle determiningportion for eachof lthese different phase angles would be required. Insuch a case, each phase angle determining portion would adjust the phaseangle resistor contacts for only those generating units which feed thebus section having the phase angle applied -to that portion. Such a casewould also require the use of separate K resistor-adjusting knobs foreach bus section having a substantially different K ratio. yEach of suchknobs would adjust the K resistor contacts for only those unitssupplying the bus section having the corresponding K ratio. These caseswould representthe equivalent of having at the same physical locationtwo or more electrically separate plants.

23 OPERATION OF THE FIG. 2 APPARATUS Initial adjustments In thepractical utilization of the Fig. 2 apparatus as the controlling portionfor Plant 1 of the Fig. l system, the K resistors 28, 30, etc. must beproperly adjusted initially in accordance with the actual, numericalvalue of the constant ratio K1 0, as was mentioned hereinbefore. Inother words, the knob 37 must be initially manually positioned asnecessary to make the eective resistances of the resistors 28, 30, etc.all equal to a particular resistance value which is individual to, orcorresponds to, the particular numerical value of K1 0. Such initialsetting of the proper K resistance value into the Fig. 2 apparatus isrequired in order to cause the balance deviation signals to be zero whenPlant l is actually in economic balance.

The proper resistance value T for the K resistors 23, 30, etc.corresponding to the existing value of K can be determinedmathematically for any given arrangement by developing a 'suitableequation relating T and K. The following is the derivation of such anequation, from which the value of T can be readily determined for anygiven value of K.

If the resistance of one half of the entire phase angle slide wireresistor 29 is designated as S, and if it is assumed that the span ofthe adjustment of the contact 31 along the entire length of the resistor29 covers sixty electrical degrees on each side of the zero centerposition, the balance equation for the bridge circuit of section 22 canbe written as:

Substituting Equation 5 into the economic balance Equation 4 gives:

S0 00184K 60(T-|s)-K2+0.17 SKL-1.lO4SKIO.17S=l.lO4KT T K2- 1.1O4J-l-0.17 1.1041( With any convenient design value chosen for and assigned toS, Equation 6 provides the proper resistance value setting T forresistors 2S, 30, etc. as a function of the value of the ratio K.

Another initial adjustment which must be made to the Fig. 2 apparatus isthe proper setting of the reference gen erating cost resistors 32, 232,etc. in the respective sections 22, 23, etc. All of these resistors areinitially set manually, by means of their corresponding knobs, to haveequal eiective resistances, the valve of this common resistance beingrepresentative of the chosen arbitrary value F0 of the generating costat the common reference point o. Similarly, all of the equivalent Foresistors at Plants 2 and 3 are initially set to have this common valueof resistance. This gives the original basis on which all plants arecompared to a common point, and hence are compared to each other.

As was mentioned previously herein, the reference generating costresistor for each generating unit7 such as the resistor 32 for unit i9,is desirably utilized as a means for permitting the incrementalgenerating cost value produced in the corresponding section to becompensated for changes in the cost of fuel at the plant from the costoriginally assumed in proportioning the corresponding incrementalgenerating cost resistor, such as the resistor 33. Each generating costresistor is also desirably utilized to compensate the correspondingcomputed incremental generating cost value for changes which affect theoperating efficiency of the corresponding generating unit and itsassociated equipment, and which hence cause the unit to operate with adifferent characteristic from that on which the design of thecorresponding characterized cam was based. Thus, the referencegenerating cost resistor for each generating unit is desirably utilizedas a means for taking into account the eiects of changes which affectthe established relationship between the effective resistance of thecorresponding incremental generating cost resistor and the output of thecorresponding generating unit.

in accordance with the foregoing, the setting or effective resistancevalue of the resistor 32 is desirably changed in practice, from theoriginal common Fo value to which all of such resistors were initiallyset, as necessary to take into account any changes in the cost of fuelat Plant l for unit 19, and to allow for changes in condenser backpressure, boiler slagging, condition of fuel, turbine clearances, an-dany other factors which affect the elhciency of the unit 19. Similarly,the setting of the resistor 232 is desirably changed in the above mannerto compensate for any of the above changes which aiect generating unit20. It is desirable to provide such a separate adjustment for the Foresistor of each unit since conditions affecting one unit do not alwaysatfect the other units in the same manner or at all, and hence do notalways require the same corrective setting to be made to all of the F0resistors.

Operation When and as long as the scheduled system requirements, such astie line loads and system frequency, are met by the existing systemgeneration, the phase of the common reference signal at Plant l, and ateach of the other plants remains constant. Under this condition, nochanges in the governor settings or the generating unit outputs are madeat Plant l or at any of the plants as long as all of the plants areloaded in the most economical manner and hence are in economic balance.

The occurrence of any change, at Plant l or elsewhere, which causesPlant 1 to deviate from economic balance, causes operation of thegovernor motors 50 and 250, and readjustment of the outputs of units 19and 20, and any other units at Plant l, as necessary to restore Plant lto economic balance with the other plants. Such restora* tion may alsoinvolve the changing of the outputs of one or both of the other systemplants. All of this may occur, however, without any departure from thescheduled system requirements, and hence without any change in the phaseof the common reference signal.

Moreover, the occurrence of changes in system load pattern, which mayoccur while the total system requirements remain satisfied, will resultin increases in the output of one or more of Plants l, 2, and 3, and/ ordecreases in the output of one or more of these plants, as necessary torestore between the plants the economic balance which was disrupted bythe load pattern change. Also, the interruption of a transmission linewill change the relative bus voltage phase angles at one or more of theplants, will temporarily destroy the economic balance between theplants, and will hence result in the adjustment of the plant outputs asnecessary to restore economic balance. Such operation will always besuch as to reduce the emergency loadings on the remaining lines, thusaiding system stability and minimizing thermal overloading.

` Upon any of the foregoing or other occurrences which cause Plant l todepart from economic balance with respect to the reference point and theother plants, the resulting operation or rotation of thegovernor-adjusting motors 5ft, 259, etc. is reduced or terminated ineach of sections 22, 23, etc. in the following two ways, each of whichreduces the deviation signals across the galvanometers:

(l) The resultant opening or closing of each turbine valve, resultingfrom the operation of the corresponding governor motor, changes theeffective resistance of the corresponding incremental generating costresistor in the direction to re'balance the corresponding bridgecircuit.

(2) "The resulting 'increase 'or v'decrease Lin vthe plant output, dueto the adjustment of each of the kturbine valves, changesthe `busvoltage-phase'angle ofthe plant, and causes ,the corresponding phaseangle resisto-r contact to be adjusted in the direction'to vrebalan'cethe corresponding vbridge circuit.

Upon the occurrence of a change in lthe system which resultsin adeviation 'between the desired or scheduled lsystemcondition values andthe actual, existing values of these conditions, the'phase of the commonreference signal'isadvanc'ed or retarded, depending on .th'e directionof the deviation. 'For example, an increase in system load, resulting ina kschedule Vdeviation requiring an increase in system generation,causes the phase of the reference signal at allplants .to ybe advanced.'This in turn unbalances the bridge circuits at .theplants and resultsin theapplication `of output raising governor adjustments to those unitsoperating near the raisesidesof the dead bands of their vgovernor motorcontrollers.

As in the case described above, such governormotor operationis reduced.or .terminated `by ythe resulting changes produced in theetectiveresistances of the incremental generating'cost resistors,Vandfby the resulting changes produced inthe positions of the phaseangle re sistor contacts by the resulting changes in the phase angles.of the plant bus voltages. Each of -these'changes is in the directionto rebalance the Vbridge circuits at the .-plants. Also, in this case,the resulting increase .in system generation may cause the phase angleof the reference signal -to ybe retarded at each plant, resulting y.in afurther `adjustment .of Vthe phase angle resistor contacts in thedirection to rebalance the bridge circuits.

.A change in system conditions resulting yin a schedule deviation'requiring a decrease insystemgeneration causes the phase of thereference signal at each plant to be retarded. This in turn causes theoutputs -of 'the appropriateplants lto be reduced, such reductions againserving to produce eiects in the direction to rebalance the bridgecircuits and reduce to vzero 'the deviation signals. In each case, theyplant; loads are assigned and reassigned until the system requirementsare met, and until the plants are loaded in the most economical mannerand hence operate in economic balance with each other.

It should be noted that yit is not 'necessary to provide automatic loadcontrol at all of the system plants, or for all of the generating unitsat any one plant. Thus, if desired, manual economic loading can beemployed at one or more plants o-r for one or more units at a givenplant. Such manual control can be eiected -by controlling manually theoutputs of the chosen plants or units in accordance with the observeddeviation indications provided by the bridge outp-ut galva'nometers, asnecessary to reduce these deviations to zero. Alternately, thevreference signal received at a chosen plant can be utilized to actuatean indicating phase meter showing the phase angle by which the plant busvoltage leads the reference signal. The plant units can then be loadedmanually by the use of tables which indicate the economic loading for'each unit for each value of said phase angle.

THE APPARATUS OF FIG. 3

Fig. 3 illustrates the details of apparatus according to the presentinvention which can be used to advantage at the dispatching otce l ofthe Fig. l arrangement for advancing and retarding the phase of thecommon reference signal in accordance with system schedule deviations.As shown, the apparatus at the dispatching ofce 1 includes atelemetering receiver '72 which receives the data as to the actualvalues of the system conditions as telemetered to the olce 1 over thechannel 16. Also included at the oice 1 is a schedule deviation detector73 which positions a contact 74 along a schedule deviation slide Wireresistor 75 through a suitable mechanical linlrage 76in accordance withthernagnitude -`anddirection of any deviation between `tht rctualandscheduled values of ithe system "condi-tions. To vthis end, Zthe outputthe"rec`eiver 72 is applied to the deviation detector '73, as is thedata as tothe scheduled values of the 'system ,conditions supplied over'the path 17. 4Since the construction and operation of such vscheduledeviation d`e`tectorsis well known, no'furthe'r description of thedetector 73-isdeemed`to befnecessary herein.

The deviation resistor "75 is included in a bridge circuit 77, theoutput of which controls the operation of a reversible .motor 7.8. Thismotor loper-altes through `Va .suitable mechanical linkage 79 to adjusta yphase shifter Sil which'in turn changes the .phase of the commonreference signal as long as the motor l".78 is rotating and hence aslong as there is Va 'schedule deviation detected .by the Adetector 73.To this end, -the reference vvoltage y'supplied to the oice lover lthepath .18 is applied to the .input terminals .81 .of the phase shifter.88, whilethe .common-reference signal is taken from the phase shifteroutput terminals 82 and is fed `by conductors 83 to the finput terminals84 .of a telemetering transmitter 85 for ,transmission over the channell5 to the Plants l, 2, and 3.

In yaddition tothe deviation resistor 75, the bridge circuit 77 includesinput or energizing terminals 86 and 87 abetween which ythetres'is'tor75 is connected, and also in cludes resistors 878 an-d 89 which areconnectedin series between the energizing terminals 86 and 87. Thelatter are arranged to `Ibe connected `to a suitable `source ofenergizing voltage, not shown. A first bridge output termi'nal 590 isconnected Ito the VContact 74 of the refsi's't'o'r 75, and a secondbridge output terminal 9i is gformed by the jun'ction'of the resistors88 and 89.

The motor '78 is controlled 4*by a galvanometer 92 which is connectedbetween the bridge output terminals '90 and 9,"and which'controls themotor '78 in accordance w'it'h the output of the bridge 77 in the sameway that the yIno'tor 50 `of the Fig. ZYapparatus is controlled by 'thegalvanometer 46 in accordance lwith the output of 'its bridge circuit.Thus, the rgalvanometer 92 is also of the zero-center, proportional'control type, and is connected between the 'bridge 'circuit outputterminals 9i) and 91 series with a condenser 93. VA resistor 94 is'connected 'across the galvanometer 92, and a resistor 95 is 'connectedacross the condenser 93. As in the case of the galvanometer 46 of Fig.2, the co-ndenser 93 and resistors 494 'and 95 'cooperate with thegalvanometer 92 to cause the `pointer deflection thereof to beproportional to both the Vmagnitude and the rate of change of the bridgeoutput signal. Thus, the deflection of the pointer ofthe galvanometer 92is proportional to both the magnitude and the rate of change of anysystem schedule deviation. A

As in the case of the galvanometer 46 and the motor 50 of Fig. '2, thegalvanometer 92 controls the motor 78 through a suitable relay 96, whichis connected between the galvanometer 9 2 and the motor 78 by suitableconductors 97. Thus, the motor 78 adjusts the phase shifter 80, andhence shifts the phase 4of the common reference signal, in one directionor the other, depending upon the direction of .galvanometer pointerdeflection, the polarity of the bridge unbalance signal, and thedirection of the system schedule deviation. Also, the speed or rate atwhich the phase shifter is adjusted by the motor 78, and hence the speedor rate at which the phase angle of the reference .signal -is advancedor retarded, is proportional to the extent and the rate of change ofbridge unbalance, and to the magnitude and the rate of change of systemschedule deviation. When there is no schedule deviation, and .hence nobridge output, the motor 78 is not energized: for rotation in eitherdirection.

Summarizing the foregoing operation, the contact 74` The resultingbridge unbalance or output signal energizes the galvanometer 92, whichcontrols the motor 78 to shift the phase angle of the reference signalat a rate proportional to the potential across the galvanometer, andhence at a rate proportional to both the magnitude and the rate ofchange of system schedule deviation.

Accordingly, there is provided at the dispatching office 1, and sent toall of the system plants, a common reference signal which is advanced inphase when the system frequency and/ or the tie line loads deviate fromschedule in the direction requiring an increase in the systemgeneration, and which is retarded in phase when the schedule deviationis such as to require a decrease in system generation. In both cases,the rate of change of the reference signal phase angle is proportionalto both the amount and the rate of change of the system scheduledeviation.

It is noted that, if desired, the means for controlling the operation ofthe motor 78 and the adjustment of the phase shifter 80 in response tothe output of the bridge 77 and the position of the deviation contact 74may be of forms other than the proportional controlling galvanometerarrangement shown herein by way of example. Thus, this means could wellbe of the form of any of the well known so-called proportional plusreset controllers which are available on the market. The particular typeof control equipment to be used for any specific situation depends onthe factors and conditions particular to that situation.

THE ARRANGEMENTS OF FIGS. 4 AND 5 The apparatus of Fig. 2, operating inaccordance with economic balance Equation 4, operates with a high degreeof accuracy nothwithstanding the substantial differences between thevalues of the different K ratios which exist throughout the usualsystem. However, certain system patterns may justify special treatmentif the systems contain a generating plant which is joined by a singletransmission line to an intermediate point on the system other than thecommon reference point, and if there is a substantial difference betweenthe value of K between the plant and the intermediate point, and thevalue of K between the intermediate point and the common referencepoint. In such cases, it may be desirable, in order to obtain therequisite operating accuracy, to perform the economic balance comparisonfor the plant in two sucr cessive steps, each step employing its ownphase angle and ratio K. One of these steps covers the economiccomparison between the plant and the intermediate point, and the othercovers the economic comparison between the intermediate point and thereference point.

In order to carry out the foregoing operation, it is necessary toaugment the Fig. 2 equipment at the plant, such as the arrangements 21and 22, with additional apparatus for providing an effect at the plantof the equivalent generating cost at the intermediate point relative tothe arbitrary reference generating cost at the reference point. Suchapparatus, operating in conjunction with the Fig. 2 apparatus at theplant, provides the foregoing economic comparison between theintermediate and reference points, while the Fig. 2 apparatus effectsthe economic comparison between the plant and the intermediate point.Thus, all of this apparatus cooperates to control the plant output in`the most economical manner by effecting the foregoing two economiccomparisons.

There is illustrated in Fig. 4 a portion of the Fig. 2 apparatus for thePlant 1 which has been modified by the addition of apparatus forpermitting the economic balance comparison for Plant 1 to be effected intwo steps, as explained above. Thus it is assumed for explanatorypurposes that Plant l in the Fig. 4 setting is a plan having thecharacteristics noted above which make it desirable to perform theeconomic comparison for the plant in two steps. Accordingly, withrespect to Fig. 4, it is assumed that Plant 1 is connected by a singletransmission path to an intermediate system point x, that the latter iscon- .nected to the reference point o, and that the value of th ratio K1 is substantially different from the value of the ratio KPD.

A typicalsystem configuration including a Plant l, a point x, and acommon reference point o, all related in the manner just described, isillustrated in Fig. 5. This figure shows the intermediate system point xlocated between the Plant 1 and the common reference point o, and showsthe single transmission path X -1 joining Plant 1 to point x. Thus, thesystem pattern shown in in Fig. 5 is typical of the type of patternreferred to above which may, and is assumed herein to, justify thespecial treatment afforded by augmented apparatus of the type shown inFig. 4.

In addition to the former control section 22 and the phase angleIdetermining portion 21 of Fig. 2, the Fig. 4 apparatus at Plant 1includes a section 122 and a phase angle determining portion 121. Thesection 122 is substantially identical to the section 22, but effectsthe economic comparison between the intermediate point x and thereference point o, using the values of the phase angle 6*, 0 and theratio K. As the result of this comparison, section 122 provides anoutput or a shaft position which is a function of the equivalentgenerating cost at point x relative to the reference point o. The valueof the phase angle 0,10 is supplied to the section 122 by the phaseangle determining portion 121, which is arranged and operative toprovide this value in the same manner as that described above inconnection with the portion 21 of Fig. 2. Therefore, that descriptionneed not be repeated a this point. f

Because of the substantial identity between the portion 121 and itscounterpart 21, and between the section 122 and its counterpart 22, theelements of the portion 121 and the section 122 bear the same referencecharacters as the corresponding elements in the portion 21 and thesection 22 of Fig. 2, but in the one-hundreds series. Further, theportion 21 and section 22 of the Fig. 4 arrangement utilize the samereference characters as in Fig. 2.

In the Fig. 4 arrangement, the :section 22 effects the economic balancecomparis-on between the Plant l and the point x in the same manner inwhich this section effects the comparison directly between Plant l andthe reference point in Fig. 2. Also, section 22 in Fig. 4 controls theoutput of the Plant 1 generating units 19', etc. exactly as in the Fig.2 arrangement. Since the section 22 of Fig. 4 is arranged to effect theeconomic balance comparison between Plant l and point x, instead ofbetween Plant 1 and reference point o, the phase angle determiningportion 21 of Fig. 4 supplies the section 22 with the value of the phaseangle 0, 1.

Also, the arbitrary generating oost resistor 32 of section 22 is not setin accordance with the arbitrary reference generating cost at thereference point as it is in Fig. 2. Instead, the contact 39 of thisresistor is positioned by the aforementioned shaft position provided bythe section 122. Acc-ordingly, the effective resistance of the resistor32 is set in accordance with the value of the equivalent generating costFx for point x as determined by the section 122.

To this end, the output linkage or shaft 153 of the section 122 isconnected to adjust the contact 39 in the section 22. A knob, pointer,and scale arrangement 93 is provided to permit the contact 39 to be`adjusted relative to the position of the shaft 153, and henceindependently of the generating cost value FX, as necessary tocompensate the section 22 for the various changes which affect theincremental generating cost value determined by the section 22, asdescribed hereinbefore. n

Since the construction and operation of the portion 21 and the section22 in the Fig. 4 yarrangement are the same as described hereinbefore inconnection with the Fig.. 2 arrangement, except for the differences justdescribed, it is not deemed to be necessary to repeat the foregoingdescription at this point.

29 The section 122 `To the end Vof positioningthe shaft @1543 and thecost resistor contact '39 in accordance with the value of the equivalentgenerating costFX, thesection122 is arranged as .a `self-balancingbridgecircuit. Thus, the motor 150, vcontrolled by the bridge outputdeviation, Yis `arranged to ,positionthe contact 144 alongthepresistor133, through Ythe linkage or shaft -153, as vnecessary vto maintain thebridgein balance. Accordingly, the position ofthe contact 144 along thekresistor 133 represents the value lof the cost Fx, and this position,and value are imparted to the contact 39 in the section 2,2,by the,shaft 153. A scale `and pointer arrangement'99 lis includedtoprovide adesirable indicationl of Ythe value of FX.

OPERATION vOF THE FIG. 4 APPARATUS lI eceiiie'sa signal, over atelemetering channel ,1115, which .is representativeof the phase ofthe-,voltage at point x.

.lnstead of employing-telemetering to supply the value of the pointervoltagephase to Plant 1, this value may be ,obtained from `an impedance-unit .at Plant 1 which ,re- ,ceives current-from the transmission lineconnecting Plant 1 to point x. The portion '1,21 supplies to the section122 the existing value of the `phaseangle ,0& `between the voltage atthepoint x and the reference signal.

The ,phase angle determining portion 21'receives the above signal havingthe phase of the Vvoltage at point x, and also receives the -signal fromthe .plant 'bus having the phase -oftheplant 1bus voltage. The portion21 supplies to the section l22 the existing .value .of the phase angle 51 vbetween the voltage at the point x yand the Plant 1 -bus voltage.

The valueofthe.constant ratio K offor points x and o is set into thesection 122 :by means of ythe `knob 137, l.while-the value of theconstant yratio `K14 is set linto the section 22 by `means .of the knob37. Thus, the value ,of the incremental transmission loss ratio forpoints x and o is computed .by the section 122, while this yvalue forVPlant 1 Iand point x is co-mputed .by the section 22. The result of the.combined operation `of the sections 22 and 122 is that the effectiveincremental transmission loss ratio for Plant l relative to point o iscompu-ted as the ,combination of the incremental transmission loss fromPlant -l to `point jc and the incremental transmission loss from pointbc to the reference point o. This operation is effected by .theapparatus vin two steps, each step employing its own value of phaseangle 0 and ratio K.

The foregoing settings of the knobs and 137 to introduce into theapparatus the values of the tw-o K ratios are desirably made in the samemanner as that described above in connection with the setting of the`knob 37 of the Fig. 2 apparatus. Similarly, the value of the arbitraryreference generating cost Fois set into the sectio-n 122 of Fig. 4 bythe vuse of the knob 41 inthe same mannervas for the "Fig, 2arrangement.

By virtue of the foregoing, the motor 150, in positioning the resistorycontact 144 as necessary to maintain the bridge circuit of section y122balanced, positions this contact in accordance with the value of theequivalent generating .cost Fx at point x .corresponding to thearbitrary -value of generating cost F0 at the reference point o. Thus,lthe position .of the .contact 144 represents the value of Fx.

This computed value of Fx is introduced into the section 22 by the shaftY153 and the resistor contact 39 adjueted thereby. Section 2,2 relatesthe value of the Plant jl incremental' generating cost, represented bythe effective resistance of the resistor 33, to the Value of theequivalent generating eest Fx, represented by the eieetive resistanceofthe resistor 32 and coordinates this relationship with the incrementaltransmission loss ratio for 30 Plant 1 relative to point x. This resultsin the control andoperation of Plant las required to cause this-plant tobe in economic balance with the reference point o, and to be loaded inthe most economical manner.

'It is noted in connection with the foregoing that, even for a plantwhich has the characteristics .and location of Plant l in Figs. 4 and 5,it is seldom worthwhile to take the special corrective steps provided bythe Fig. 4 apparatus unless the system fuel relationships are such thatthe voltage phase angle .at point x is substantially less (or greater)than the bus voltage phase angle at Plant 1, or the reference phaseangle for point o. That is, if the bus Vo-ltage at Plant 1 normallyleads the voltage at point X, and the voltage at point x normally leadsthe reference signal, the need for the corrective action provided by theFig. 4 apparatus is minimized.

In connection with the foregoing, it is noted that apparatus of the typewhich constitutes the section 122 can desirably be utilized, for otherthan the correcting purposes for which it is utilized in the Fig. 4arrangement, to provide its measure or indication of the value or costof incremental energy or power at a desired, given point in the system.Thus, this apparatus of the type forming the section 122, plus thenecessary phase .angle determining portion, such as the portion 121, canbe utilized at any convenient location for the purpose of providing atthat location an indication of the incremental value or cost of energyat a given point in the economically balanced system. This point may ormay not be at said location.

Such use of apparatus of this type is possible by virtue of the factthat, whenever Plants 1, 2, and 3 are in economic balance, the positionof the Contact 144 on the resistor l133, and the reading on the scale99, provide a direct indication of the incremental value of energy atpoint x. That is, for system balance, the resistance from point 127 tocontact 144 represents, in terms of the calibration of the Fo resistor132, the incremental cost of generation of la hypothetical plant atpoint x which would be in economic balance with Plants 1, 2, and 3.Accordingl'y, such apparatus will function to determine, for aneconomically balanced system, the value or cost of energy Vat any givenpoint in the system, such as an interconnection point with anothersystem or area.

Such use of this apparatus requires, at the location where it isutilized, data as to the phase of the voltage of the commo-n referencesignal from the dispatcher, the phase of the voltage at the given pointfor which the apparatus is to determine the value of energy, the valuenf K for the transfer impedance between the systemreference point andsaid given point, and the commen arbitrary value of generating cost Fofor the reference point. This data is the same as that shown applied tothe section 122 in its use as a correcting arrangement in Fig. 4.

It is apparent that the apparatus of the portion 122, when used as anincremental energy value indicato-r for a given system point as justdescribed, may be located at the given point, at the dispatching office1, or at any other convenient location. When this given point is aninterconnection point with another area or company, the incrementalenergy value indication provided by this apparatus will serve to provideoptimum schedules of generation and interconnection flows.

CONCLUSON By virtue of the use of the foregoing reference pointcomparison equation and method as the basis for the operation of thedisclosed apparatus, the latter possesses many features of practicalsignificance, as shonid be readily apparent in the light of theforegoing description. For example, such use permits the use ofrelatively simpie apparatus at each plant for effecting the economicbalance deviation detecting and deviation signal producing operations,as well as the economic assignment of the plant loads. Such use alsopermits the dispatching office

